[Dune-devel] [GSoC2016]B-Spline geometry - current progress

[Xinyun Li]

Hello all,

I am writing to to let you know my current progress on the B-Spline
geometry interface and propose some of my doubts.

I modified the B-Spline basis function calculation.  Instead of building
the whole pyramid to get the basis functions we need on the top level, we
can build an inverted triangular to merely compute the non-zero functions.
Later, we only need to multiple these non-vanishing values with the
corresponding control points, which is more efficient. In addition, I
implemented a simple working NURBS geometry interface and added some test
code in the main file. I tested on my computer, they both look fine.

Now I'm working on other interface functions. I have implemented the
following functions:
GeometryType  type () const;
bool affine () const;
int corners () const;
GlobalCoordinate corner (int i) const;
GlobalCoordinate center () const;

All the codes are available via
https://gitlab.dune-project.org/Xinyun.Li/dune-iga. I will be very grateful
if you can review my code as some of my thoughts may possibly be wrong.The
next step is  Jacobian related function. I have written some pseudocode and
have got a clue on it. So hopefully I can finish it this week or early next
week.

My doubts
1. How to implement the following functions?
ctype volume() const.
LocalCoordinate local(const GlobalCoordinate&) const;
I don't know how to define the volume of the B-Spline structure and the
inverse mapping from the physical space to the element space also seems
non-trivial.
2. Matrix operation
I will need the transpose and pseudo-inverse of a matrix. I think these
functions should already been implemented in DDUNE. I had a quick look of
the FieldMatrix class but not sure if it is enough.

Thanks for your time in advance.

Best regards,
Xinyun
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